During the collisions of two nuclei at relativistic energies it is expected to form a hot and dense state of matter known as Quark Gluon Plasma (QGP) which is governed by light quarks and gluons [1]}. Heavy quarks, namely charm (\(c\) ) and bottom \((b)\)  quarks are considered one of the fine probes of quark gluon plasma (QGP). Due to the fact that their masses \((M)\)  are significantly larger than the QCD energy scale (\(\Lambda _\text{QCD}\) ) and the temperature (\(T\) ) at which QGP is created i.e \( M >> \Lambda _\text{QCD}, T\) . Unlike the light quarks they do not thermalize quickly and witness the entire evolution of the fireball. Currently, it is admitted that a very strong magnetic field is created at very early stage of heavy-ion collisions [2]}, [3]}. The estimated values of the intensity of the strong magnetic field created at RHIC and LHC is of the order of \(10^{18}\)  to \(10^{19}\)  Gauss [4]}. The effects of such a strong magnetic field is discussed in different cases such as jet quenching coefficient \(\hat{q}\)  [5]}, elliptic flow [6]}, chiral magnetic effect [7]} etc. The effect has also been studied to diffusion coefficients of charm quarks [8]}, [9]}. As heavy quarks produced early in the heavy-ion collisions their dynamics can be affected by such strong magnetic field.
In this article we aim to study the longitudinal and transverse components of diffusion coefficients of heavy quarks in a QGP medium in the presence of a background magnetic field \(\vec{B}\)  in \(z\) -direction.
